Connie Rossini’s Is Centering Prayer Catholic is an excellent source to see a critique regarding Centering Prayer. What I really liked is the distinctions she makes and how she compares the various statements made by the late Fr. Thomas Keating compared to what St. Teresa of Avila wrote regarding contemplative prayer. She really is trying to be as fair as possible, and does an excellent job of explaining the problems along with also accurately explaining what authentic Catholic contemplative prayer is.
Previously I have looked into some of Fr. Thomas Keating writings and statements and found them problematic. This book does a good job of focusing on the claims of the centering prayer movement.
This book also makes good caveats. For example what people might encounter under the umbrella of centering prayer, might actually be something much closer to authentic Catholic contemplative prayer. There is a good amount of confusion regarding what exactly centering prayer is as understood by some people practicing it compared to what the centering prayer movement advocates.
She also uses the document Jesus Christ the Bearer of the Water of life, a Christian reflection on the “New Age”, to compare the concerns raised with the statements of the centering prayer movement. This new edition answers objections raised by Contemplative Outreach, the organization started by the founders of the centering prayer movement.